Let \(H\)  be \(\sum _{i=1}^{[\frac{n-1}{2}]}H_{2i+1}\) , where \(H_{2i+1}\) 
is a closed \((2i+1)\) -form. Then one can define a new operator
\(D=d+H\)  on \(\Omega ^{\ast }(M)\) , where \(H\)  is understood as an
operator acting by exterior multiplication (for any differential
form \(w\) , \(H(w)=H\wedge w\) ). As in [1]}, [2]}, there is a
filtration on \((\Omega ^{\ast }(M),D)\) :
\(K_p=F_p(\Omega ^{\ast }(M))=\bigoplus \limits _{i\ge p}\Omega ^i(M).\) 
